Localization

Question 1

What is localization?

Answer 1

The problem of estimating the robot’s position given a map
of the environment and a sequence of sensor readings.

Question 2

SLAM

Answer 2

SLAM stands for Simultaneous Localization and Mapping. It is a method used by robots and autonomous vehicles to understand and map their environment while simultaneously determining their own location within it.

Question 3

How SLAM ideally works

Answer 3

The robot would observe the world zt1, move a small amount and observe zt2. Since zt1 and zt2 overlap, the robot merges the two into a map and then localize itself in the new map.

The new map represents the maximum likelihood of the world.

The problem is that the robot not always moves as expected.

Question 4

Define the SLAM problem

Answer 4

Given:

• robots controls: u1:T
• observations: z1:T

Wanted:

• map of the env: m
• path of the robot (or the actual position): x0:T

Question 5

Probabilistic localization

Answer 5

Uncertainty in the robot’s motions and observations. Use the probability theory to explicitly represent the uncertainty.

Question 6

Probabilistic map-based localization

Answer 6

Identify probabilities with the possible robot positions.

Two methods for probabilistic map-based localization:

• Markov localization
• Kalman filters localization

Question 7

Robot localization problem (position uncertanty from growing unbounded)

Answer 7

Consider a mobile robot that is moving and keeping track of its position using odometry. In order to keep position uncertanty from growing unbounded, the robot must localize itself in relation to its environment map.

Information of proprioceptive (predictive or action phase) and extroceptive sensors (perception or measurement or correction phase) can be combined for localize the robot.

Question 8

Classification of localization problems

Answer 8

• position tracking: current location is given by the previous location
• global localization: initial position is not given
• kidnapped robot problem

Question 9

Terminology in SLAM

Answer 9

• path: Xt = {x0, …, xt}
• proprioceptive measurements: Ut = {u0, …, ut}
• exteroceptive measurements: Zt = {z0, …, zt}
• map: M = {m_0, …, m_n-1} (n-1 landkmark vectors)
• belief distribution: bel(xt) = p(xt | z1->t, u1->t)

Question 10

Probabilistic motion model

Answer 10

Is derived from the kinematics of the robot:

xt = f(xt-1, ut)

where xt-1 is the previous location and ut is the encoder readings.

Question 11

Probabilistic measurement model

Answer 11

Derived from the exteroceptive sensor model:

p(zt | xt, M)

Question 12

Markov localization

Answer 12

Address the problems of position tracking, global localization and the kidnapped robot problem.

Example with unkown initial position:
1. prediction update: initial belief = uniform probability distribution (so no convolution) -> compute probabilistic measurement model
2. perception update -> find the new belief
3. moving…
4. prediction update: new belief by convolution -> compute probabilistic measurement model
5. perception update -> find the new belief
6. repeat from 3…

Question 13

Kalman filters

Answer 13

Uses the sensor fusion technique.

Addresses only the position tracking problem since it starts by imposing the initial belief with a Gaussian probability distribution.

Example similar to the Marvov localization one.